This coterminal angle calculator converts an angle in degrees or radians into two positive co-terminal angles and two negative co-terminal angles.

Coterminal Angle Formula

The following formulas are used to calculate coterminal angles.

Positive Coterminal Angle = Angle + 360

Negative Coterminal Angle = Angle -360

The formulas above would only yield one of each co terminal angles. In reality, there is an infinite number of co-terminal angles. The definition is simply an angle that ends at the same point as another angle on a coordinate plane. Since the coordinate circle has a total rotation of 360 degrees, adding or subtracting that to the angle yields a result as does the coterminal angle calculator above.

To calculate a coterminal angle between 0 and 2π, in terms of pi, you must add or subtract 2π from the fractional pi value given. For example:

Find the coterminal angle of 11π/3:

Since 11π/3 > 2π, subtract 2π from the given angle. If the given angle was less negative, you would add 2π.

11π/3 – 2π/1 = 11π/3 – 6π/3 = 5π/3.

Coterminal Angle Definition

A coterminal angle is an angle that ends at the same geometric point on the coordinate plane as another angle.

Common Coterminal Angle Values

The following list outlines the coterminal angles of the most commonly calculated angles.

  • Coterminal angles of -225 = 135 and -585 degrees
  • Coterminal angles of -90 = 270 and -450 degrees
  • Coterminal angles of -150 = 210 and -510 degrees
  • Coterminal angles of 112 = 472 and -248 degrees
  • Coterminal angles of -45 = 315 and -405 degrees
  • Coterminal angles of -304 = 56 and -664 degrees
  • Coterminal angles of 153 = 513 and -207 degrees
  • Coterminal angles of 56 = 416 and -304 degrees
  • Coterminal angles of -60 = 300 and -420 degrees
  • Coterminal angles of 320 = 680 and -40 degrees
  • Coterminal angles of -70 = 290 and -430 degrees
  • Coterminal angles of 128 = 488 and -232 degrees
  • Coterminal angles of 166 = 526 and -194 degrees

How to calculate a co terminal angle

Let’s take a look at an example of how you might calculate the coterminal angle.

  1. Let’s assume you are given an angle in radians. For this example, the angle is 2.5 radians.
  2. First, you must convert the radians to degrees. 1 radian is equal to 57.29 degrees so 2.5*57.28=114.59 degrees
  3. Last, we need to add 360 degrees to that angle to find an angle that is coterminal with the original angle, so 114.59+360 = 475.59 degrees.
  4. Check the answer using the calculator above.

FAQ

What is a coterminal angle?

A coterminal angle is an angle that ends at the same location as another angle. For example, 1 degree and 361 degrees are at the same location since the total angles in a circle are 360 degrees.

What is the coterminal angle formula?

The coterminal Angle can be calculated with one of the following:
Positive Coterminal Angle = Angle + 360
Negative Coterminal Angle = Angle -360